MinT - Best Known (10, 26, s)-Nets in Base 32

Best Known (10, 26, s)-Nets in Base 32

(10, 26, 104)-Net over F₃₂ — Constructive and digital

Digital (10, 26, 104)-net over F₃₂, using

t-expansion [i] based on digital (9, 26, 104)-net over F₃₂, using
- net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(10, 26, 113)-Net over F₃₂ — Digital

Digital (10, 26, 113)-net over F₃₂, using

net from sequence [i] based on digital (10, 112)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 10 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(10, 26, 150)-Net in Base 32 — Constructive

(10, 26, 150)-net in base 32, using

4 times m-reduction [i] based on (10, 30, 150)-net in base 32, using
- base change [i] based on (5, 25, 150)-net in base 64, using
  - 3 times m-reduction [i] based on (5, 28, 150)-net in base 64, using
    - base change [i] based on digital (1, 24, 150)-net over F₁₂₈, using
      - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
        a function field by SÃ©mirat [i]

(10, 26, 172)-Net in Base 32

(10, 26, 172)-net in base 32, using

2 times m-reduction [i] based on (10, 28, 172)-net in base 32, using
- base change [i] based on digital (2, 20, 172)-net over F₁₂₈, using
  - net from sequence [i] based on digital (2, 171)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 2 and N(F) ≥ 172, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(10, 26, 9460)-Net in Base 32 — Upper bound on s

There is no (10, 26, 9461)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1362 225564 491789 113864 829370 224073 096542 > 32²⁶ [i]